arXiv subjects

E. Gourgoulhon

Publications and source records attributed to E. Gourgoulhon.

57 records · Page 4Linked to original sources

arXiv1996

Gravitational waves from pulsars: emission by the magnetic field induced distortion

The gravitational wave emission by a distorted rotating fluid star is computed. The distortion is supposed to be symmetric around some axis inclined with respect to the rotation axis. In the general case, the gravitational radiation is emitted at two frequencies: $Ω$ and $2Ω$, where $Ω$ is the rotation frequency. The obtained formulæ are applied to the specific case of a neutron star distorted by its own magnetic field. Assuming that the period derivative $\dot P$ of pulsars is a measure of their magnetic dipole moment, the gravitational wave amplitude can be related to the observable parameters $P$ and $\dot P$ and to a factor $β$ which measures the efficiency of a given magnetic dipole moment in distorting the star. $β$ depends on the nuclear matter equation of state and on the magnetic field distribution. The amplitude at the frequency $2Ω$, expressed in terms of $P$, $\dot P$ and $β$, is independent of the angle $α$ between the magnetic axis and the rotation axis, whereas at the frequency $Ω$, the amplitude increases as $α$ decreases. The value of $β$ for specific models of magnetic field distributions has been computed by means of a numerical code giving self-consistent models of magnetized neutron stars within general relativity. It is found that the distortion at fixed magnetic dipole moment is very dependent of the magnetic field distribution; a stochastic magnetic field or a superconductor stellar interior greatly increases $β$ with respect to the uniformly magnetized perfect conductor case and might lead to gravitational waves detectable by the VIRGO or LIGO interferometers. The amplitude modulation of the signal induced by the daily rotation of the Earth has been computed and specified to the case of the Crab pulsar and VIRGO

astro-ph↗

arXiv1995

Spontaneous Symmetry Breaking of Rapidly Rotating Stars in General Relativity

We investigate the effects of general relativity upon the non-axisymmetric ``bar'' mode secular instability of rapidly rotating stars, i.e. the relativistic and compressible analog of the transition from Maclaurin spheroids to Jacobi ellipsoids. Our method consists in perturbing a stationary axisymmetric configuration, constructed by a 2-D general relativistic numerical code, and taking into account only the dominant terms in the non-axisymmetric part of the 3-D relativistic equations. For a polytropic equation of state, we have determined, as a function of the degree of relativity, the critical adiabatic index $γ_{\rm crit}$ above which rapidly rotating stars can break their axial symmetry. A by-product of the present study is the confirmation of the Newtonian value $γ_{\rm crit} = 2.238$ obtained by James (1964). We have also considered neutron star models contructed upon twelve nuclear matter equations of state taken from the literature. We found that five equations of state from this sample allow the symmetry breaking for sufficiently high rotation velocities. For the others, the Keplerian velocity (mass-shedding from the equator) is reached before the axisymmetry is broken. Rotating neutron stars that break their axial symmetry can be an important source of gravitational waves for the LIGO/VIRGO interferometric detectors.

gr-qc↗

arXiv1995

ROTATING NEUTRON STAR MODELS WITH MAGNETIC FIELD

We present the first numerical solutions of the coupled Einstein-Maxwell equations describing rapidly rotating neutron stars endowed with a magnetic field. These solutions are fully relativistic and self-consistent, all the effects of the electromagnetic field on the star's equilibrium (Lorentz force, spacetime curvature generated by the electromagnetic stress-energy) being taken into account. The magnetic field is axisymmetric and poloidal. Five dense matter equations of state are employed. The partial differential equation system is integrated by means of a pseudo-spectral method. Various tests passed by the numerical code are presented. The effects of the magnetic field on neutron stars structure are then investigated, especially by comparing magnetized and non-magnetized configurations with the same baryon number. The deformation of the star induced by the magnetic field is important only for huge values of B (B>10^{10} T). The maximum mass as well as the maximum rotational velocity are found to increase with the magnetic field. The maximum allowable poloidal magnetic field is of the order of 10^{14} T (10^{18} G) and is reached when the magnetic pressure is comparable to the fluid pressure at the centre of the star. For such values, the maximum mass of neutron stars is found to increase by 13 to 29 % (depending upon the EOS) with respect to the maximum mass of non-magnetized stars.

gr-qc↗